Pexeso

Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?

Correct result:

x₁ =  60 mm
x₂ =  40 mm

Solution:

$$\begin{gathered} a=60\text{ cm}\to \text{ mm}=60\cdot 10\text{ mm}=600\text{ mm } \\ b=840\text{ mm } \\ 600=2^3\cdot 3\cdot 5^2 \\ 840=2^3\cdot 3\cdot 5\cdot 7 \\ \text{GCD}(600,840)=2^3\cdot 3\cdot 5=120 \\ y=GCD(a,b)=GCD(600,840)=120 \\ 30<x<100 \\ {x}_1=y\mathrm{/}2=120\mathrm{/}2=60\text{ mm} \end{gathered}$$

$x_2=y\mathrm{/}3=120\mathrm{/}3=40\text{ mm}$

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